41
Manhole Flotation
Introduction
The proper functioning of a sewer system is
dependent to a large degree on the performance of its
appurtenances, and especially its manholes. As with
many buried structures, the proper design of manholes
should take into account the effect of the water table
and its specific effect on installation and operating
conditions.
Figure 1
Manhole Installations
Cross Section of Extended Base
Manhole Installation
The Buoyancy Concept
From a fluid dynamics standpoint, the buoyant force
acting on a submerged object is equal to the weight of
fluid which that object displaces. In the case of a buried
structure or manhole, this concept is applicable when a
high ground water table or other subaqueous condition
exists. As with the design of buried pipe, flotation should
be checked when conditions such as the use of flooding
to consolidate backfill, flood planes or future man-made
drainage changes are anticipated.
Extended
Base
Cross Section of Smoothwall
Manhole Installation
Manhole Buoyancy Analysis
Vertical manhole structures of two types (Figure
1) are generally constructed, and each type should be
considered when analyzing the flotation potential. The
first case to be considered is a structure in which the
base does not extend past the walls of the manhole.
This structure will be called a smooth-wall manhole
installation. Smooth-wall manholes utilize the weight of
the structure itself and the downward frictional resistance
of the soil surrounding the manhole to resist the upward
buoyant force. Some manufacturers and designers use
an extended base to provide additional resistance to
buoyant forces. These structures are constructed with
a lip extending beyond the outer edges of the manhole
and are termed extended base manhole installations. An
extended base manhole uses the additional weight of
soil above the lip as well as its self-weight and frictional
forces to resist flotation.
Design methods, using basic soil mechanics to
determine if a manhole is susceptible to flotation, are
presented here to aid the engineer in their design of the
structure.
Shear Strength
For an installed and backfilled structure to actually
Base
Flush with
Exterior
Surface
“float”, or exhibit upward movement, the buoyant forces
must overcome both the weight of the structure and the
shear between the walls and the soil. Shear strength is
defined in soils engineering to be the resistance to sliding
of one mass of soil against another. Shear strengths,
as typically provided, are a measure of the resistance
to sliding within a single uniform soil mass. The shear
strength of a soil has traditionally been related by two
strength parameters: internal friction and cohesion.
Shear strength ( τ f ) as typically expressed by
Coulomb’s equation is:
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DD 41 May 2008
τf = c + σ (tan φ)
where:
τf
=
c =
φ =
σ =
shear strength, lbs/ft2 (kPa)
cohesion, lbs/ft2 (kPa)
angle of internal friction, degrees
normal stress on the sliding surface or
shear plane, lbs/ft2 (kPa)
Certain analyses require shear strength between
dissimilar substances, most commonly soil and concrete.
This shear strength is an apparent rather than true shear
resistance and is usually called sliding resistance.
Sliding resistance equations typically use a coefficient
of friction (f) to represent the friction between the two
dissimilar materials. The equation for sliding resistance
is therefore defined as:
rsliding = c + σ f
Cohesionless Soils
A uniform cohesionless soil (sands and gravels) by
definition has a cohesion coefficient, (c), equal to zero.
The sliding resistance equation, therefore, reduces to:
rsliding = c + σ f
Several different references are available which
address values for the coefficient of friction. Typical
values of the friction coeffficient (f) from the literature
generally range between .35 for silts and .55 for coarsegrained gravels against concrete. The friction coefficient
is a function, however, of soil material type, manhole
material, outside manhole profile, compaction levels,
and material homogeneity. The designer is cautioned to
solicit site specific materials properties and appropriate
design values for individual projects from professionals
in the geotechnical field.
Table 5.5.5B of the American Association of State
Highway and Transpor tation Officials (AASHTO)
Standard Specification for Highway Bridges, 15th Edition
(1992), lists friction factors for soil materials against
concrete. The values in Table 1 are taken from Table
5.5.5B of AASHTO.
Normal Pressure
In order to quantify the sliding resistance, it is
necessary to determine the lateral pressure on the walls
of the manhole. Assuming the top of the manhole to be
at ground surface, the vertical earth pressure is equal
to zero at the surface and varies as a function of the soil
density with depth to the base. Since the engineer is
concerned with flotation, we will initially look at the case
where the ground water surface is even with the top of
the manhole.
Because a high groundwater condition is being
analyzed, the designer must determine the effective
weight of soil solids which are buoyed up by the water
pressure. This submerged soil weight becomes less than
that for the same soil above water and is given by:
γsub = γs
where:
1-
1
S.G.
γsub
= effective unit weight submerged,
lbs/ft3 (N/m3)
γs = unit weight of dry soil,
lbs/ft3 (N/m3)
S.G = Specific Gravity of the soil,
dimensionless
Specific gravity is based only upon the solid portion of
a material. Soil is a conglomerate of minerals, all having
differing specific gravities, and containing voids between
the soil grains. For this analysis, a specific gravity for the
soil particles as they occur naturally will be used. Specific
gravity ranges from 2.50 to 2.80 for most soils, with a
majority of soils having a specific gravity near 2.65.
Vertical manhole structures normally experience ring
compression and therefore are subject to active earth
Table 1
Ultimate Friction Factors and Friction Angles for Dissimilar Materials from AASHTO Table 5.5.5B
Interface Materials
Friction
Angle, δ
(Degrees)
Friction
Factor, f
tan δ (DIM)
Formed concrete or concrete sheet piling against the following soils:
• Clean gravel, gravel-sand mixture, well-graded rock fill with spans ................ 22 to 26 ......... 0.40 to 0.50
• Clean sand, silty sand-gravel mixture, single size hard rock fill ...................... 17 to 22 ......... 0.30 to 0.40
• Sllty sand, gravel or sand mixed with silt or clay..................................................17 ................... 0.30
• Fine sand silt, nonplastic silt ................................................................................14 ................... 0.25
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DD 41 May 2008
pressures. The magnitude of the normal pressure, at a
given depth (d) is determined by both the effective weight
of the soil pushing against the wall of the structure and
the water pressure caused by the submerged condition
(Figure 2). This normal force is given by the following
equation:
σ = (Ka γsub + γw) d
where: σ
Ka
d
γ
w
= Normal stress against wall, lbs/ft2
(kPa)
= Active lateral earth pressure
coefficient, dimensionless
= Depth at which normal pressure
acts, ft (m)
= Unit weight of water, 62.4 Ibs/ft3
(9.8 kN/m3)
However, water exerts a negligible friction force on
the wall of the manhole. Therefore, the normal stress
considered for friction is based on the effective vertical
stress:
σ = (Ka γsub) d
where: σ =
Effective normal stress against wall,
lbs/ft2 (N/m2)
Estimates of active lateral earth pressure vary with
soil type. Marston’s values included in Table 3, as well
as commonly accepted values, indicate that a lateral
earth pressure coefficient of 0.33 is adequate for most
soil materials.
Sliding Resistance
The total sliding resistance available to resist
flotation at a given depth (d) is the combination of the unit
resistance (rsliding) acting over the exterior circumferential
surface of the manhole.
The assumptions of uniform soil material and ring
compression for the structure make the unit resistance
equal at a given depth around the circumference of the
structure. The unit resistance available at depth (d) is
therefore defined as:
rsliding = σ (f) (π) (Bd)
where: (π) (Bd) = circumference of manhole,
ft (m)
f
= friction factor, dimensionless
Since the vertical and lateral pressure, and hence
the unit sliding resistance, varies with depth, the sliding
resistance available for the total structure, Rsiding, is equal
to the summation of the various rsiding values over the
height (H) of the structure from the ground surface to the
bottom of the base slab.
d
Figure 2
Manhole
Magnitude of
Earth Pressure
at "d"
H
+
γ sub (H)(K a)
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γw (H)
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DD 41 May 2008
H
Rsliding =
Σ
d
With P defined, Rsliding can be calculated as:
(rsliding)
Rsliding = P (f) (π) (Bd)
0
Since the pressure exerted varies linearly with depth
from 0 at the ground surface to (Ka γsub)H at the manhole
base, (Figure 3) the total resultant pressure acting on the
manhole can be defined as:
P = [(Ka
γsub) H ]
H
NOTE: The lateral pressure (γ)(H) reaches a maximum
limit at approximately 15 Bd. Most manhole installations
are not that deep. However, lateral pressure must be
considered for extremely deep installations.
2
Figure 3
h= 2/3H
H
h
Manhole
Bd
Groundwater Level Effect
In order to design for the most conservative case and
also simplify the design procedure, the groundwater level
was earlier assumed to exist at the top of the manhole
structure. If the designer is assured that the groundwater
surface is below grade level, and will remain there, the
design procedure can be modified accordingly.
For a structure where the groundwater surface is
below grade level (Figure 4) the effective unit weight
of the soil will vary above and below the groundwater
surface. Since the groundwater level affects the
magnitude of the normal forces at various depths, these
force are calculated in separate parts as follows:
=
P
γ sub (H)(K a )
Pdry = [(γs) (Y ) (Ka) ]
Y
2
Zone B - the total effective force of the earth against
the wall below the water table
1 (γ )(H-y)(K )
Psub = (H-y) [(γs)(y)(Ka)] +
sub
a
2
The sliding resistance can be found from:
Rsliding = (Pdry + Psub) (f)(π)(Bd)
Zone A - the total soil force from the ground level to
the water table;
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DD 41 May 2008
Y
Figure 4
H
Manhole
H-Y
γ s (Y)(K a )
+
+
Bd
γ s (Y)(K a )
Cohesive Soils
In clays and silty soils the cohesion coefficient (c)
depends on the nature and consistency of the material.
The angle of internal friction for clays (φ) can vary from
0° to 30°. Many soils are either dominantly cohesive
or noncohesive and, for simplification in engineering
computations, are considered to be either one or
the other. Applying this assumption, the (φ) value for
completely saturated clays is zero, and the sliding
resistance equation reduces to:
γ sub (H -Y)Ka
The value of c can be derived as a fraction of the
unconfined compressive strength (qu) and is generally
represented as follows:
c =
qu
2
Typical values for the unconfined compressive
strength of clays are shown in Table 2:
rsliding = c
Table 2
Consistency
Field Identification
Unconfined
Compressive Strength
qu, psf (kPa)
Very Soft................. Easily penetrated several inches by fist ..................................Less than 500 (24)
Soft ......................... Easily penetrated several inches by thumb.............................500-1,000 (24 - 48)
Medium .................. Can be penetrated several inches by thumb
with moderate effort ................................................................1,000-2,000 (48 - 96)
Stiff ......................... Readily indented by thumb but penetrated
only with great effort................................................................2,000-4,000 (96 - 192)
Very Stiff ................. Readily indented by thumbnail ................................................4,000-8,000 (192 - 384)
|Hard ...................... Indented with difficulty by thumbnail .......................................Over 8,000 (384)
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The designer is cautioned to use site specific
values or, moreover, those determined to be valid by a
professional skilled in the determination of geotechnical
parameters. The values shown in Table 2 may not apply
to individual project conditions.
With the value of (qu) defined, Rsliding is defined as:
Rsliding = π (Bd )
qu
2
(H )
Rsliding = π (Bd ) (c) (H )
As previously stated, the buoyant force (B) is equal to
the weight of water displaced by the manhole structure.
This force is defined as the density of water multiplied
by the volume of water displaced by the structure, and
is expressed as:
Bd 2
4
W + Rsliding
B
Extended Base Manhole Installations
Buoyancy Analysis
π
F.S.buoyancy =
Generally, if the weight of the structure is the primary
force resisting flotation than a safety factor of 1.0 is
adequate. However, if friction or cohesion are the primary
forces resisting flotation, then a higher safety factor would
be more appropriate to account for the variability of the
soil properties.
or
B = γW
Keeping this relationship in mind, a design safety factor
for buoyancy is easily derived:
H
where: γw = density of water = 62.4 Ibs/ft3 (9.8 kN/m3)
Installations in which the base slab extends beyond
the outer face of the manhole wall (Figure 5) are treated
only slightly differently than the smooth-wall installations.
This case can be analyzed as a smooth-wall installation
with the following exceptions.
1) The diameter of the base (Db) should be used
instead of using the external diameter of the structure
itself (Bd) to determine the perimeter of the failure
cylinder.
2) Since the failure mode is a backfill shear failure, the
coefficient of friction (f) for granular materials should
be determined by:
Design Safety Factor
f = tan
This buoyant force (B) is resisted by the weight of the
manhole assembly (W) and the total sliding resistance
(Rsliding).
For the structure to be stable:
φ
where: φ = angle of internal friction for the backfill
material
For an initial estimate, a friction coefficient may
be taken from Table 3 which gives soil friction
W + Rsliding ≥ B
Table 3
Approximate Safe Working Values of the Constants to Be Used In Calculating the Loads on Pipes
in Ditches
Ditch Fill
w=Unit Weight
of Backfill
(lbs/ft3)
K= Ratio of
Lateral to
Vertical Earth
Pressures
u=coefficient
of Friction
Against Sides of
Trenches
90
0.33
0.50
Saturated Top Soil
110
0.37
0.40
Partly Compacted Damp Yellow Clay
100
0.33
0.40
Saturated Yellow Clay
130
0.37
0.30
Dry sand
100
0.33
0.50
Wet Sand
120
0.33
0.50
Partly Compacted Top Soil
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Figure 5
W
W
Manhole
Additional
Anchoring
Force
Provided By
Soil Above Base
Lip
Bd
Db
coefficients developed by Marston for soils placed
in a trench with a similar insitu soil.
3) The additional effective weight of the backfill in the
cylinder above the lip can be added as an anchoring
force.
The designer is advised to use caution in the analysis
of extended base structures because the parameters
employed vary greatly with material proper ties,
compaction levels, and friction factors assumed between
native and compacted soils. In the case of extendedbase structures, an alternative would be to perform the
analysis as detailed for a smooth-wall structure. Although
greatly conservative, this analysis can provide a quick
check of the particular installation against buoyancy.
Cones and Reducers
If a cone or reducer section is used for a manhole,
the designer shall calculate the total weight accordingly.
The sliding resistance for the cone or reducer section
shall be calculated as follows:
Ps = Ka
γsub (Hbot – Htop)
Hbot – Htop
2
where: Rs-sliding = Sliding resistance of the individual
section
Rs–sliding = Ps (f ) π
Ps
Hbot
Htop
Dbot
Dtop
Dbot + Dtop
2
= Resultant horizontal force on the individual
section
= Fill height to the bottom of the section
= Fill height to the top of the section
= Outside diameter of the bottom of the
section
= Outside diameter of the top of the section
This sliding resistance can then be added to the
sliding resistance of the manhole above and below the
section. (Figure 6)
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DD 41 May 2008
Figure 6
H top
D top
H
H bot
P above
=
Ps
P below
D bot
Pabove = [(Ka) γsub Htop ]
(
Htop
2
Pbelow = γsub (Ka) (H – Hbot)
)
H + Hbot
2
Rabove = Pabove (f ) (π) (Dtop)
Rbelow = Pbelow (f ) (π) (Dbot)
Rtotal-sliding = Rs-sliding + Rabove+ Rbelow
NOTE: An analysis of this detail can generally be avoided by initially assuming the entire structure has the smaller
diameter (Dtop) and calculating the factor of safety against buoyancy.
Example 1:
Given: A 60-inch (1500 mm) diameter manhole, as shown in Figure 7, is to be installed in a clean gravel-sand area to
a depth of 23 feet (7 m). The ground water table in the area fluctuates slightly, but in most cases is assumed
to be level with the ground surface. A geotechnical analysis at the site yields the following information:
Soil Type
= Clean sand
Unit Weight of Soil, γs
= 120 Ibs/ft3 (18.8 kN/m3)
Soil Specific Gravity, S.G. = 2.75
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Figure 7
Wcover = 500 lbs. (2.2 Kg)
t s = 0.67 ft. (200 mm)
H = 23.0 ft. (7 m)
Dc = 3.0 ft. (900 mm)
t w = 0.5 ft. (150 mm
D i = 5.0 ft. (1500 mm)
Bd = 6.0 ft. (1800 mm)
Find:
t b = 1.0 ft. (300 mm)
If the manhole installation is stable with respect to buoyancy, and has a minimum factor of safety of 2.0, as
required by the project engineer.
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DD 41 May 2008
Solution: (U.S. Units)
1.
Weight of the Structure
Wtotal = Wwalls + Wbase + Wtop +Wcover
Assume the unit weight of concrete, γc = 150 lbs/ft3
Wtotal = π
Bd
2
Wtotal = π
6
2
2
-
2
Di
2
(H
2
- 5
- tb - ts) γc +
2
2
(23-1 -.67)(150) +
π
2
(Bd ) (tb) γc + π
4
2
π
(6) (1)(150 ) + π
4
Bd
2
2
6
2
2
-
Dc
2
2
3
2
2
(ts) (γc) +W cover
(.67) (150) +500
Wtotal = 27,640 + 4,241 + 500
Wtotal = 34,510 lbs
2. Sliding Resistance
From Table 1 the friction coefficient (f) = .30
Assume Ka = 0.33
γsub = γs 1- 1
S.G.
P = Ka
= 120 1- 1
= 76.4 lbs/ft3
2.75
γsub (H) H
2
P = [(.33) (76.4)] (23)
Rsliding = P (f ) (π) (Bd)
23
= 6,665 lbs/ft
2
Rsliding = 6,665 (.3) (π) (6) = 37,690 lbs (downward)
3. Buoyant Force
B = γw
π
B = 62.4
(Bd)2
4
(6)
4
π
H
2
23 = 40,580 lbs (upward)
4. Factor of Safety
FS =
FS =
Wtotal + Rsliding
B
34,510 + 37,690
= 1.8 < 2.0
40,580
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The factor of safety is not great enough. Therefore, try an extended base with a 1 ft. extension around the
entire diameter.
Diameter of Base = Db = 8ft.
5. Weight of Extended Base Structure
π
Wbase =
Wbase =
4
(Db) (tb ) γc
π
(8) (1) (150) = 7,540 lbs
2
2
4
Wsoil = π
Db
Wsoil = π
8
2
2
Bd
-
2
2
-
2
2
6
2
(H-tb ) γsub
2
(23-1) (76.4) = 36,963 lbs
From Step 1:
Wwalls
Wtop
Wcover
= 27,640 lbs
= 2,131 lbs
= 500 lbs
Wtotal
= 7,540 + 36,963 + 27,640 + 2,131 + 500
= 74,774 lbs
6. Sliding Resistance
From Step 2: P = 6,665 lbs
From Table 3 for sand: f = .5
Rsliding = 6,665 (.5) (γ) (8) = 83,760 lbs (downward)
Buoyant Force
(
B = 62.4
π
(Db)2
(Bd)2
H1 + π
H2
4
4
(
π
(
(
B = γw
(
(
(
7.
(8) 2
(6)2
22 + π
1
4
4
(
B = 41,952 lbs (upward)
8. Factor of Safety
FS =
Note:
74,774 + 83,760
= 3.8 > 2.0 satisfactory condition
41,952
This example was completed to show the differences in design between a smooth-wall and extended base
manhole. Most concrete manhole producers only make either a smooth-wall or extended base manhole.
Therefore, the specifier may not have the option of adding an extended base.
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DD 41 May 2008
Solution: (Metric Units)
1.
Weight of the Structure
Wtotal = Wwalls + Wbase + Wtop +Wcover
Assume the unit weight of concrete, γc = 23.5 kN/m3
Wtotal = π
Bd
2
Wtotal = π
1.8
2
2
-
Di
2
2
- 1.5
2
2
(H
- tb - ts) γc +
2
(7-.3 -.2)(23.5) +
π
2
(Bd ) (tb) γc +
4
γ
2
π
(1.8) (.3)(23.5) + π
4
Bd
2
2
1.8
2
-
Dc
2
2
-
.9
2
2
(ts) (γc) +W cover
2
(.2) (23.5) +2.2
Wtotal = 118.8 + 17.9 + 9.0 + 2.2
Wtotal = 147.9 kN
2. Sliding Resistance
From Table 1, the friction coefficient (f) = .30
Assume Ka = 0.33
γsub = γs 1- 1
S.G.
P = Ka
= 18.8 1- 1
= 12.0 kN/m3
2.75
γsub (H) H
2
P = [(.33) (12.0)] (7) (3.5) = 96.7 kN/m
Rsliding = P (f) (π) (Bd)
Rsliding = 96.7 (.3) (π) (1.8) = 164.1 kN (downward)
3. Buoyant Force
B = γw π
(Bd)2
H
4
B = 9.81 π
(1.8) 2
7 = 174.6 kN (upward)
4
4. Factor of Safety
FS =
FS =
Wtotal + Rsliding
B
147.9 + 164.1
= 1.8 < 2.0
174.6
The factor of safety is not great enough. Therefore, try an extended base with a 0.3 meter extension around
the entire diameter.
Diameter of Base = Db = 2.4m
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DD 41 May 2008
5. Weight of Extended Base Structure
2
Wbase = π (Db) (tb ) γc
4
2
Wbase = π (2.4) (.3) (23.5) = 31.9 kN
4
Wsoil = π
Db
2
2
Wsoil = π
2.4
2
2
-
-
Bd
2
(H-tb ) γ sub
2
1.8
2
2
(7-.3) (12) =159.1 kN
From Step 1:
Wwalls
Wtop
Wcover
Wtotal
=
=
=
=
=
118.8 kN
9.0 kN
2.2 kN
31.9 + 159.1 + 118.8 + 9.0 + 2.2
321 kN
6. Sliding Resistance
From Step 2: P = 96.7 kN/m
From Table 3 for sand: f = .5
Rsliding = 96.7 (.5) (π) (2.4) = 364.6 kN (downward)
Buoyant Force
(Db)2
(Bd)2
H1 + π
H2
4
4
(
π
(
B = 9.81
(
π
(
(
(
(
B = γw
(
7.
2.4 2
(1.8) 2
6.7 + π
0.3
4
4
B = 180.6 kN (upward)
8. Factor of Safety
FS =
Note:
321 + 364.6
= 3.8 > 2.0 satisfactory condition
180.6
This example was completed to show the differences in design between a smooth-wall and extended base
manhole. Most concrete manhole producers only make either a smooth-wall or extended base manhole.
Therefore, the specifier may not have the option of adding an extended base.
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DD 41 May 2008
Example 2:
Given: The 60-inch (1500mm) diameter manhole in Example 1 (without an extended base) is to be installed in a
soft clay soil with native material used to backfill the structure. No geotechnical analysis is available for the
site.
Find:
If the manhole installation is stable with respect to buoyancy and has a minimum factor of safety of 2.0, as
required by the project engineer.
Solution: (U.S. Units)
1.
Weight of the Structure
From Example 1, Wtotal = 34,510 lbs.
2. Sliding Resistance
For cohesive soils, Rsiding = c =
qu
2
From Table 2, qu for soft clay is 500 psf.
Rsliding = π (Bd ) (H )
Rsliding = π (6 ) (23)
qu
2
500
2
=108,385 lbs
3. Buoyant Force
From Example 1, the buoyant force, B = 40,580 lbs
4. Factor of Safety
FS =
FS =
W + Rsliding
B
34,510 + 108,385
= 3.5
40,580
FSrequired = 2.0 < 3.5 satisfactory condition
Solution: (Metric Units)
1.
Weight of the Structure
From Example 1, Wtotal = 147.9 kN
2. Sliding Resistance
For cohesive soils, Rsiding = c =
qu
2
From Table 2, qu for soft clay is 24 kPa.
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DD 41 May 2008
Rsliding = π (Bd ) (H )
Rsliding = π (1.8 ) (7)
qu
2
24
2
= 475 kN
3. Buoyant Force
From Example 1, the buoyant force, B = 174.6 kN
4. Factor of Safety
FS =
FS =
W + Rsliding
B
147.9 + 475
174.6
= 3.5
FSrequired = 2.0 < 3.5 satisfactory condition
References:
1.
AASHTO Standard Specifications for Highway Bridges, Fifteenth Edition, 1992
2. Principles of Geotechnical Engineering, Braja M. Das, PWS-Kent Publishing Company, 1985
3. Soil Engineering (Fourth Edition), Merlin G. Spangler and Richard L. Handy, Harper & Row, Publishers,
1982
4. Soil Mechanics in Engineering Practice, Karl Terzaghi and Ralph B. Peck, John Wiley & Sons, Inc., 1966
5. The Theory of Loads on Pipes in Ditches and Tests of Cement and Clay Drain Tile and Sewer Pipe, A.
Marston and A. O. Anderson, Iowa State College of Agriculture and Mechanic Arts, 1913
American Concrete Pipe Association • www.concrete-pipe.org • [email protected]
Technical data herein are considered reliable, but no guarantee is made or liability assumed.
15
DD 41 May 2008